It is advantageous in radio, sonar and some other communications systems to develop samples of base-band in-phase and quadrature components of an input bandpass signal. A bandpass signal of center frequency f.sub.IF can be demodulated into baseband by mixing with a complex sinusoidal signal e.sup.j2 P.pi. t of frequency f.sub.IF. The resulting baseband signal is a complex signal with a real, or "in-phase" component represented by I, and an imaginary, or "quadrature", component represented by Q. Once a bandpass signal is demodulated into its in-phase and quadrature components, various commonly used modulation schemes such as amplitude (AM), frequency (FM), single-side-band (SSB), and quadrature-amplitude-phase modulations can be extracted by simple arithmetic operations. For example, the upper side-band of a SSB modulated signal can be extracted by adding the I and Q components together. Furthermore, it is advantages especially when data communication is involved, to digitized the output to produce digital output samples of the I and Q components.
FIG. 1 is a block diagram showing a conventional analog circuit for demodulating the in-phase (I) in quadrature (Q) components of an input analog signal. The analog signal is received on input line 10, which is then split into in-phase line 12 and quadrature phase line 14. Cosine mixer 16 mixes the analog input signal with a cosine signal (at the center frequency of the pass-band of the input signal) and provides the mixed signal along line 18 to low pass filter (LPF) 20, which attenuates undesirable image by-products of the mixing. The filtered signal is provided along line 22 to analog-to-digital converter (ADC) 24 which converts the analog signal to in-phase samples at a sampling rate f.sub.s and provides the in-phase samples I on bus 26.
Similarly, sine mixer 28 mixes the input analog waveform with a conventional sine wave and provides the mixed signal on line 30 to LPF 32. LPF 32 attenuates undesirable image by-products of the mixing and provides the filtered signal on line 34 to ADC 36. ADC 36 converts the filtered signal to digital quadrature samples at a sampling rate f.sub.s and provides the quadrature output samples Q on bus 38.
The circuit of FIG. 1 has a number of drawbacks and constraints. For example, the circuit is difficult to implement. The sine and cosine waveforms must be exactly 90.degree. out of phase with each other in order to produce accurate in-phase and quadrature samples. In data communication, mismatches in the sine and cosine phases will result in bit errors. In addition, the two mixers must have good linearity to avoid mixing in spurious frequency components.
FIG. 2 is a block diagram of another prior art approach which addresses some of the drawbacks and constraints of the circuit of FIG. 1. The circuit of FIG. 2 performs the out-of-phase mixing of the input waveform in the digital domain, avoiding the use of a problematic analog multipliers and providing tight control over the sine and cosine waveforms. The analog input waveform is received on line 10 and converted to a digital signal by ADC 40. The digital signal is provided on buses 44 and 45. Digital multiplier 46 multiplies the converted samples received on bus 44 with cosine-wave samples (i.e., coefficients) and provides the multiplied samples on bus 48 to decimator 50. Decimator 50 conventionally decimates, or downsamples, the cosine-multiplied samples and provides in-phase samples (I) on output bus 52.
Similarly, digital multiplier 54 multiplies the samples received on bus 46 by sine-wave samples and provides the multiplied samples on bus 56 to decimator 58. Decimator 58 downsamples the sine-multiplied samples and provides quadrature (Q) output samples on bus 60. Decimator 58 operates at the same rate as does decimator 50. The drawbacks of this approach are the complexity and cost of the digital-signal-processing and in the need for high-speed, high-resolution ADC.
FIG. 3 is a block diagram showing an improved implementation of the circuit of FIG. 2 using a sigma-delta ADC for which f.sub.s =4.times.f.sub.IF where f.sub.s is the sampling frequency of the sigma-delta ADC and f.sub.IF is the center frequency of the pass-band of the analog input waveform. The sigma-delta ADC provides a one-bit digital stream at an oversampling rate and performs noise-shaping such that the quantization noise power is shifted to frequencies outside of the band of interest. As will be understood by those skilled in the art, four evenly-spaced samples of a cosine signal may equal the set of values {1, 0, -1, 0}; and four corresponding evenly-spaced samples of a sine waveform, being 90.degree. out of phase with the cosine waveform, then will have values {0, -1, 0, 1}. These sampled (i.e., coefficient) values are used, respectively, by the multipliers 46 and 54, in the prior art circuit of FIG. 3, as the cosine and sine samples which are multiplied with the input signal. Multiplication by such a limited set of coefficients (i.e., 1, 0 and -1) can be implemented simply with conventional logic, as will be appreciated by those skilled in the art.
While the digital circuit of FIG. 3 does provide advantages over the analog circuit of FIG. 1, in terms of increasing the simplicity and performance of the multipliers, the system suffers from a number of drawbacks. Specifically, because the frequency of the input waveform must be 1/4 that of the sampling frequency (or similarly related), the oversampling ratio (OSR) of the sigma-delta ADC is limited. This places a great demand on the anti-aliasing filter (not shown) which precedes the circuit to reduce low frequency components of the input waveform before conversion. The oversampling ratio (OSR) for a band-pass sigma-delta ADC is defined as the sampling frequency f.sub.s divided by twice the bandwidth f.sub.BW of the input waveform: OSR=f.sub.s /2f.sub.BW. A typical example includes an input waveform having a center frequency IF=455, kHz having a bandwidth f.sub.BW 30 kHz, and a sigma-delta converter having a sampling rate f.sub.s =1.8 MHz. In this example, the oversampling would be equal to approximately 30, which is quite small. As a result, the signal-to-noise ratio of the output samples is relatively low and may not be acceptable for accuracy reasons.